Question

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

• A. $\frac{1}{2}M{\omega }^2{L}^2$
• B. $M{\omega }^{2}L$
• C. $\frac{1}{4}M{\omega }^{2}L$
• D. $\frac{1}{2}M{\omega }^{2}L$

Answer 1

Answer: (D)

The force exerted by liquid at the other end is the centripetal force due to rotation. The case can be treated as rotation of the center of mass of the liquid at distance $L/2$ from the axis of rotation.

Hence force exerted by liquid at the end $=M{\omega }^2\left(\frac{L}{2}\right)$ $=\frac{1}{2}M{\omega }^{2}L$